A large number of two dimensional puzzles is known. For example, U.S. Pat. Des. Nos. 252,094 and Des. 252,091, to Popeck disclose games sets comprising a plurality of squares bearing individual designs.
U.S. Pat. Des. No. 212,242, to Paulus discloses an alphabet puzzle in which various letters of the alphabet have nesting characteristics so that they can form a rectangle when nested together.
U.S. Pat. Des. No. 238,698, to Cook discloses a puzzle in which all the pieces combine to create a square.
U.S. Pat. Des. No. 169,482, to Henke et al. discloses a display unit of interfitted toy blocks.
U.S. Pat. Des. No. 34,767, to McCaleb discloses a design for a puzzle board on which are printed squares, each of which is composed of smaller figures of angular shape and each smaller figure having a rectangular figure in or near its center, with none of the figures alike.
U.S. Pat. Des. No. 275,301, to Cloud discloses a puzzle having various pieces to form a cross.
U.S. Pat. Des. No. 272,842, to Matsumoto discloses a puzzle including various squares and rectangles.
U.S. Pat. No. 3,904,994, to Bates et al. discloses a meander line circuit with an interdigital ground plane.
U.S. Pat. No. 3,892,409, to Herbert, Jr. discloses a game employing a board divided into squares for reception of tiles, with each tile representing an element of play.
U.S. Pat. No. 4,534,563, to Guenther discloses a three dimensional puzzle having a plurality of component pieces which, when assembled, form a plurality of different right rectangular prism solution shapes.
U.S. Pat. No. 4,177,993, to Crosby et al. discloses a variable block puzzle and container containing nine blocks that must interfit in a specific way to fit into a box.
U.S. Pat. No. 4,614,344, to O'Connor discloses a game board composed of interchangeable congruent game board segments butted together randomly allowing for variation of pathways by interchanging game board segments.
Mathematical tiling problems are usually concerned with completely covering a plane surface using multiple tiles of a particular shape or shapes. Other puzzles, such as tangrams, provide a set of pieces of particular geometric shapes, with the object being to form a single geometric shape by contiguously positioning all pieces of the set.
Many of the prior art puzzles, especially the two dimensional prior art puzzles, are not sufficiently challenging for experienced puzzle players. Further, many prior art puzzles do not express significant mathematical relationships and therefore are not appealing to puzzle players with an interest in mathematics.
Accordingly, it is an object of this invention to provide a puzzle of simple conception and construction that nevertheless provides a challenging level of complexity.
It is a further object to provide such a puzzle that expresses deep mathematical relationships.
It is a further object of this invention to provide such a puzzle that can be implemented on a video display using a computer.
It is a still further object of this invention to provide such a puzzle that can be fabricated from readily available materials.